I would strip piece it similar to a log cabin block. Start with the center. Then add a strip of the triangle color and trim into a triangle. Then add 1 of the longer strips and trim flush at the ends. The outside corner triangles go last.

I would strip piece it similar to a log cabin block. Start with the center. Then add a strip of the triangle color and trim into a triangle. Then add 1 of the longer strips and trim flush at the ends. The outside corner triangles go last.

The problem is that it extends onto the other strip. It doesn't stop flush.
See what I mean? Or am I missing something?

I would strip piece it similar to a log cabin block. Start with the center. Then add a strip of the triangle color and trim into a triangle. Then add 1 of the longer strips and trim flush at the ends. The outside corner triangles go last.

This will work if you don't want it to look like the pattern downloaded. If you want it to look like the pattern this won't work because they aren't triangles, they are trapezoids.

I would strip piece it similar to a log cabin block. Start with the center. Then add a strip of the triangle color and trim into a triangle. Then add 1 of the longer strips and trim flush at the ends. The outside corner triangles go last.

The problem is that it extends onto the other strip. It doesn't stop flush.
See what I mean? Or am I missing something?

I see what you mean, you aren't missing anything. The only way I can see is to do partial seams.

You don't have to do a Y seam, but you will have to do a partial seam.

With the pink triangles, sew each one on half way (does not have to be an 'exact' stopping point.) Do all four pink triangles like this.
Now go back to any triangle. Lift up the edge that is unsewn, lay the rectangle strip down under it along the focus fabric, and sew that rectangle down along the focus fabric and along the edge of your triangle. Then you will just have to finish the triangle seams where you stopped.

You don't have to do a Y seam, but you will have to do a partial seam.

With the pink triangles, sew each one on half way (does not have to be an 'exact' stopping point.) Do all four triangles like this.
Now go back to any triangle. Lift up the edge that is unsewn, lay the rectangle strip down under it along the focus fabric, and sew that rectangle down along the focus fabric and along the edge of your triangle. Then you will just have to finish the triangle seams where you stopped.